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Simplifying 79x2 + -200x + 125 = 0 Reorder the terms: 125 + -200x + 79x2 = 0 Solving 125 + -200x + 79x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 79 the coefficient of the squared term: Divide each side by '79'. 1.582278481 + -2.53164557x + x2 = 0 Move the constant term to the right: Add '-1.582278481' to each side of the equation. 1.582278481 + -2.53164557x + -1.582278481 + x2 = 0 + -1.582278481 Reorder the terms: 1.582278481 + -1.582278481 + -2.53164557x + x2 = 0 + -1.582278481 Combine like terms: 1.582278481 + -1.582278481 = 0.000000000 0.000000000 + -2.53164557x + x2 = 0 + -1.582278481 -2.53164557x + x2 = 0 + -1.582278481 Combine like terms: 0 + -1.582278481 = -1.582278481 -2.53164557x + x2 = -1.582278481 The x term is -2.53164557x. Take half its coefficient (-1.265822785). Square it (1.602307323) and add it to both sides. Add '1.602307323' to each side of the equation. -2.53164557x + 1.602307323 + x2 = -1.582278481 + 1.602307323 Reorder the terms: 1.602307323 + -2.53164557x + x2 = -1.582278481 + 1.602307323 Combine like terms: -1.582278481 + 1.602307323 = 0.020028842 1.602307323 + -2.53164557x + x2 = 0.020028842 Factor a perfect square on the left side: (x + -1.265822785)(x + -1.265822785) = 0.020028842 Calculate the square root of the right side: 0.141523291 Break this problem into two subproblems by setting (x + -1.265822785) equal to 0.141523291 and -0.141523291.Subproblem 1
x + -1.265822785 = 0.141523291 Simplifying x + -1.265822785 = 0.141523291 Reorder the terms: -1.265822785 + x = 0.141523291 Solving -1.265822785 + x = 0.141523291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.265822785' to each side of the equation. -1.265822785 + 1.265822785 + x = 0.141523291 + 1.265822785 Combine like terms: -1.265822785 + 1.265822785 = 0.000000000 0.000000000 + x = 0.141523291 + 1.265822785 x = 0.141523291 + 1.265822785 Combine like terms: 0.141523291 + 1.265822785 = 1.407346076 x = 1.407346076 Simplifying x = 1.407346076Subproblem 2
x + -1.265822785 = -0.141523291 Simplifying x + -1.265822785 = -0.141523291 Reorder the terms: -1.265822785 + x = -0.141523291 Solving -1.265822785 + x = -0.141523291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.265822785' to each side of the equation. -1.265822785 + 1.265822785 + x = -0.141523291 + 1.265822785 Combine like terms: -1.265822785 + 1.265822785 = 0.000000000 0.000000000 + x = -0.141523291 + 1.265822785 x = -0.141523291 + 1.265822785 Combine like terms: -0.141523291 + 1.265822785 = 1.124299494 x = 1.124299494 Simplifying x = 1.124299494Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.407346076, 1.124299494}
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